{"title":"Localized version of hypergraph Erdős-Gallai Theorem","authors":"","doi":"10.1016/j.disc.2024.114293","DOIUrl":null,"url":null,"abstract":"<div><div>The weight function of an edge in an <em>n</em>-vertex uniform hypergraph <span><math><mi>H</mi></math></span> is defined with respect to the number of edges in the longest Berge path containing the edge. We prove that the summation of the weight function values for all edges in <span><math><mi>H</mi></math></span> is at most <em>n</em>, and characterize all extremal hypergraphs that attain this bound. This result strengthens and extends the hypergraph version of the classic Erdős-Gallai Theorem, providing a local version of this theorem.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24004242","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The weight function of an edge in an n-vertex uniform hypergraph is defined with respect to the number of edges in the longest Berge path containing the edge. We prove that the summation of the weight function values for all edges in is at most n, and characterize all extremal hypergraphs that attain this bound. This result strengthens and extends the hypergraph version of the classic Erdős-Gallai Theorem, providing a local version of this theorem.
期刊介绍：
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
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